Mass-loss rate as a function of luminosity. Various mass-loss rate relations derived for red supergiants are shown for a fixed stellar mass of 10 M_⊙ (left panel) and of 25 M_⊙ (right panel) for an assumed effective temperature of 3450 K (Reimers 1975; de Jager et al. 1988; Nieuwenhuijzen & de Jager 1990; Salasnich et al. 1999; van Loon et al. 2005; Beasor et al. 2020; Goldman et al. 2017; Kee et al. 2021). Empirical mass-loss rate relations are displayed with a solid line, the theoretical relation of Kee et al. (2021) is shown with a dashed line for 2 different values of the atmospheric turbulent velocity . For the empirical relation of Goldman et al. (2017), we use the RSG period–luminosity relation as given in Eq. (C.17) of De Beck et al. (2010), which is valid for pulsation periods between ∼300 and 800 days. The corrected Ṁ_SED-relation based on the data of Beasor et al. (see Eq. (6)) is shown as dotted grey line; the new Ṁ_CO-relation derived from the ALMA CO(2–1) measurements of the M-type RSG winds in RSGC1 (Eq. (8)) is shown as full red line. The rate at which hydrogen and helium are consumed by nuclear burning are shown as thick dashed-triple dotted lines; the single-scattering radiation pressure limit for an expansion velocity of 12 km s⁻¹ is shown as dashed dark grey line. Stellar mass loss rules the evolution of RSG stars if the wind mass-loss rate exceeds the nuclear burning rate, as indicated by the light-blue region; the nuclear-burning dominated region is indicated by the light-orange region. The red triangles in the right panel indicate the (L, Ṁ)-values as derived in Sect. 3.1 from the ALMA CO(2–1) line profiles of F01, F02, F03, F04, and F13.